In the present paper we have explored the applicability of ST to
systems displaying anomalous diffusion. We have studied two important
cases, namely Markovian systems with time-dependent noise strength
(such as SBM), and FBM. The latter provides a paradigmatic example of
a non-Markovian process yielding anomalous diffusion, where the
non-Markovianity stems from the noise correlation
function. Methodologically, we have essentially followed the
definitions and derivations of ST quantities and the IFR for standard
Brownian systems [1]}. Not surprisingly, the treatment of
FBM turned out to be challenging.
